Better results can be obtained if the FC collects all the reports and estimate the state vector as a whole. In a cognitive radio scenario, for instance, this corresponds to decide about spectrum occupancy over an entire time window, or, more realistically, to jointly decide about the state of the spectrum at different frequency slots. As an example, the FC may try to identify the malicious nodes by measuring the similarity (or dissimilarity) between the submitted reports and use such an estimate to ignore the reports coming from suspect nodes in the decision fusion process. Such an approach, which is usually referred to as Byzantine isolation [1]}, is adopted in [2]}. According to such a work, all the components of the state vector are analyzed to assign to each node a reputation measure which is eventually used to isolate the byzantine nodes, which are identified as the nodes with a low reputation. A different isolation scheme based on adaptive learning is described in [3]}, where the observed behavior of the nodes is compared with the expected behavior of honest nodes. A peculiarity of this scheme is that it works even when the majority of the nodes are byzantine, but it requires very long state vectors to achieve good performances. Better performance can be obtained if some additional knowledge about the Byzantine behavior is available, as in [4]}, where the knowledge about \(P_{mal}\)  and the number of Byzantines in the networks is exploited to develop a soft isolation scheme. As in [5]}, a game theoretic approach is used to determine the optimum strategies for the Byzantines and the FC. This corresponds to determining the optimum value of \(P_{mal}\)  for the Byzantines and the value of some internal parameters of the isolation scheme for the FC. As in that work,
it turns out that setting \(P_{mal} = 1\)  is a dominant strategy for the Byzantines.
Tolerant schemes which mitigate the impact of Byzantines in the decision, instead of removing them, have also been proposed, like in [6]}, where the reports are weighted differently according to the reputation score of the nodes.
